Building Acoustics

Sound absorbers 161

ref

()

p() 20lg

px

Lx

p

⎛⎞

=⋅⎜⎟

⎝⎠





,

and exhibiting alternating maxima and minima, is shown in Figure 5.4. It should be
noted that the equations above does not take into account any possible energy losses in
the medium in front of the specimen. The figure, which is reproduced from the standard,
gives however a much too exaggerated picture of how the ratio of the maximum and
minimum varies along the tube. Obviously, the point here is to make one aware of this
effect, which certainly must be observed when performing accurate measurements.

Test specimen

Lp(x)

Loudspeaker

xmin1 x

min2

Figure 5.4 Standing wave pattern in the test tube.

5.3.2 Standing wave tube. Method using transfer function (ISO 10534–2)

The classical method is based on measurements on a standing wave having just one
frequency component. We may obtain the same results by representing the sound
pressure and particle velocity as simple functions of time. We can use an arbitrary time
function to set up a sound field in the tube and then use the Fourier transform to revert to
the frequency domain. As an example, we may represent the pressure reflection factor at
an arbitrary position x in the tube as being the transfer function having the pressure pi in
the incident plane wave as the input variable and the pressure pr^ in the reflected wave as
the output variable:

{ }

{}

r

i

F(,)

(, )

F(,)

pxt

Rx f

pxt

= , (5.5)

where F symbolizes the Fourier transform. The basic idea is to express the relationship
between the wave components at two (or more) positions along the tube. Doing this it
may be shown that we are able to make separate estimates of the intensity in the incident
and the reflected wave. In fact, to determine the variables we shall be interested in, it is
sufficient to measure one single transfer function, namely between the total pressure in
two positions. Using Figure 5.5 as a starting point, we shall give a short description of
the procedure. At two positions, having coordinates x 1 and x 2 , we define